30.12.12 problem 12

Internal problem ID [7604]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 04:54:50 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 25

ode:=3*diff(diff(y(t),t),t)+11*diff(y(t),t)-7*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{\frac {t \sqrt {205}}{3}}+c_2 \right ) {\mathrm e}^{-\frac {\left (11+\sqrt {205}\right ) t}{6}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 38

ode=3*D[y[t],{t,2}]+11*D[y[t],t]-7*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-\frac {1}{6} \left (11+\sqrt {205}\right ) t} \left (c_2 e^{\frac {\sqrt {205} t}{3}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-7*y(t) + 11*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{\frac {t \left (-11 + \sqrt {205}\right )}{6}} + C_{2} e^{- \frac {t \left (11 + \sqrt {205}\right )}{6}} \]